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Class: AP Calculus

Ron Reimer

H.S. AP Calculus

Overview:

“Mathematics is the language that God used to write the universe.”  This quote from Galileo expresses the goal of all the math courses I teach at Immanuel.   Mathematics is a gift from God to man that allows men to grasp His rationality.   Calculus is the mathematics of the infinite.  The class begins by examining the limit concept which is then used to develop the derivative and the integral

Topics to be covered:

  • – The limit concept
  • – Definition
  • – Rules for finding limits
  • – One and two sided limits
  • – Infinite limits
  • – Continuity
  • –  The derivative
  • –  Definition
  • –  Differentiation Rules
  • –  Special case derivatives
  • –  The chain rule
  • –  Trig, Inverse trig, logarithmic and exponetial derivatives
  • –  Implicit differentiation
  • –  Applications of derivatives
  • –  Increasing and decreasing, concavity
  • –  Relative and Absolute Extrema}
  • –  Related Rate and Optimization Problems
  • – The integral
  • – Defintion
  • – The fundamental theorm of calculus
  • – Simple Integration
  • – Integration by u-substitution}
  • – Integration by parts}
  • – Logarithmic integration
  • – Applications of integration
  • – Areas and Volumes
  • – Summing Rates